Oliver also referred to Thiry as a "showboating musketeer" who "dresses like an idiot" and made fun of his love of the Leonardo DiCaprio film "The Man in the Iron Mask." (It is a comedy show after all.)

But Oliver ended his segment with a plea to viewers to donate their kidneys and other organs.

He even suggested the hashtag #whenidietakemykidneys, which trended on Twitter Sunday night and Monday morning. (HBO is a sister company of CNNMoney. Both are owned by Time Warner.)

But a spokesperson for DaVita said in a statement to CNNMoney that "we are proud of our differentiated clinical outcomes, our teammates' dedication to patient care and our strong culture."

DaVita added that "our teammates are passionate about delivering high-quality patient care and enabling our patients to live fulfilling lives."

"We will continue to advocate for our patients and invest in our teammates and our culture," the company said.

Fresenius(FMS), a German-based owner of dialysis companies that was also mentioned on the show, was not immediately available for comment. Shares of both companies fell Monday though.